A broad range of on-line behaviors are mediated by interfaces in which people make choices among sets of options. A rich and growing line of work in the behavioral sciences indicate that human choices follow not only from the utility of alternatives, but also from the choice set in which alternatives are presented. In this work we study comparison-based choice functions, a simple but surprisingly rich class of functions capable of exhibiting so-called choice-set effects. Motivated by the challenge of predicting complex choices, we study the query complexity of these functions in a variety of settings. We consider settings that allow for active queries or passive observation of a stream of queries, and give analyses both at the granularity of individuals or populations that might exhibit heterogeneous choice behavior. Our main result is that any comparison-based choice function in one dimension can be inferred as efficiently as a basic maximum or minimum choice function across many query contexts, suggesting that choice-set effects need not entail any fundamental algorithmic barriers to inference. We also introduce a class of choice functions we call distance-comparison-based functions, and briefly discuss the analysis of such functions. The framework we outline provides intriguing connections between human choice behavior and a range of questions in the theory of sorting.
{"title":"Comparison-based Choices","authors":"J. Kleinberg, S. Mullainathan, J. Ugander","doi":"10.1145/3033274.3085134","DOIUrl":"https://doi.org/10.1145/3033274.3085134","url":null,"abstract":"A broad range of on-line behaviors are mediated by interfaces in which people make choices among sets of options. A rich and growing line of work in the behavioral sciences indicate that human choices follow not only from the utility of alternatives, but also from the choice set in which alternatives are presented. In this work we study comparison-based choice functions, a simple but surprisingly rich class of functions capable of exhibiting so-called choice-set effects. Motivated by the challenge of predicting complex choices, we study the query complexity of these functions in a variety of settings. We consider settings that allow for active queries or passive observation of a stream of queries, and give analyses both at the granularity of individuals or populations that might exhibit heterogeneous choice behavior. Our main result is that any comparison-based choice function in one dimension can be inferred as efficiently as a basic maximum or minimum choice function across many query contexts, suggesting that choice-set effects need not entail any fundamental algorithmic barriers to inference. We also introduce a class of choice functions we call distance-comparison-based functions, and briefly discuss the analysis of such functions. The framework we outline provides intriguing connections between human choice behavior and a range of questions in the theory of sorting.","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130876151","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the stochastic matching problem, we are given a general (not necessarily bipartite) graph G(V,E), where each edge in E is realized with some constant probability p > 0 and the goal is to compute a bounded-degree (bounded by a function depending only on p) subgraph H of G such that the expected maximum matching size in H is close to the expected maximum matching size in G. The algorithms in this setting are considered non-adaptive as they have to choose the subgraph H without knowing any information about the set of realized edges in G. Originally motivated by an application to kidney exchange, the stochastic matching problem and its variants have received significant attention in recent years. The state-of-the-art non-adaptive algorithms for stochastic matching achieve an approximation ratio of 1/2-ε for any ε > 0, naturally raising the question that if 1/2 is the limit of what can be achieved with a non-adaptive algorithm. In this work, we resolve this question by presenting the first algorithm for stochastic matching with an approximation guarantee that is strictly better than 1/2: the algorithm computes a subgraph H of G with the maximum degree O(log(1/p)/p such that the ratio of expected size of a maximum matching in realizations of H and G is at least 1/2 + δ0 for some absolute constant δ0 > 0. The degree bound on H achieved by our algorithm is essentially the best possible (up to an O(log(1/p)) factor) for any constant factor approximation algorithm, since an Ω(1/p) degree in H is necessary for a vertex to acquire at least one incident edge in a realization. Our result makes progress towards answering an open problem of Blum et al (EC 2015) regarding the possibility of achieving a (1 - ε)-approximation for the stochastic matching problem using non-adaptive algorithms. From the technical point of view, a key ingredient of our algorithm is a structural result showing that a graph whose expected maximum matching size is OPT always contains a b-matching of size (essentially) b ... OPT, for b = 1/p.
{"title":"The Stochastic Matching Problem: Beating Half with a Non-Adaptive Algorithm","authors":"Sepehr Assadi, S. Khanna, Yang Li","doi":"10.1145/3033274.3085146","DOIUrl":"https://doi.org/10.1145/3033274.3085146","url":null,"abstract":"In the stochastic matching problem, we are given a general (not necessarily bipartite) graph G(V,E), where each edge in E is realized with some constant probability p > 0 and the goal is to compute a bounded-degree (bounded by a function depending only on p) subgraph H of G such that the expected maximum matching size in H is close to the expected maximum matching size in G. The algorithms in this setting are considered non-adaptive as they have to choose the subgraph H without knowing any information about the set of realized edges in G. Originally motivated by an application to kidney exchange, the stochastic matching problem and its variants have received significant attention in recent years. The state-of-the-art non-adaptive algorithms for stochastic matching achieve an approximation ratio of 1/2-ε for any ε > 0, naturally raising the question that if 1/2 is the limit of what can be achieved with a non-adaptive algorithm. In this work, we resolve this question by presenting the first algorithm for stochastic matching with an approximation guarantee that is strictly better than 1/2: the algorithm computes a subgraph H of G with the maximum degree O(log(1/p)/p such that the ratio of expected size of a maximum matching in realizations of H and G is at least 1/2 + δ0 for some absolute constant δ0 > 0. The degree bound on H achieved by our algorithm is essentially the best possible (up to an O(log(1/p)) factor) for any constant factor approximation algorithm, since an Ω(1/p) degree in H is necessary for a vertex to acquire at least one incident edge in a realization. Our result makes progress towards answering an open problem of Blum et al (EC 2015) regarding the possibility of achieving a (1 - ε)-approximation for the stochastic matching problem using non-adaptive algorithms. From the technical point of view, a key ingredient of our algorithm is a structural result showing that a graph whose expected maximum matching size is OPT always contains a b-matching of size (essentially) b ... OPT, for b = 1/p.","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"200 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131465018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sampath Kannan, Michael Kearns, Jamie Morgenstern, Mallesh M. Pai, Aaron Roth, R. Vohra, Zhiwei Steven Wu
We consider settings in which we wish to incentivize myopic agents (such as Airbnb landlords, who may emphasize short-term profits and property safety) to treat arriving clients fairly, in order to prevent overall discrimination against individuals or groups. We model such settings in both classical and contextual bandit models in which the myopic agents maximize rewards according to current empirical averages, but are also amenable to exogenous payments that may cause them to alter their choices. Our notion of fairness asks that more qualified individuals are never (probabilistically) preferred over less qualifie ones [8]. We investigate whether it is possible to design inexpensive subsidy or payment schemes for a principal to motivate myopic agents to play fairly in all or almost all rounds. When the principal has full information about the state of the myopic agents, we show it is possible to induce fair play on every round with a subsidy scheme of total cost o(T) (for the classic setting with k arms, ~{O}(sqrtk3T), and for the d-dimensional linear contextual setting ~{O}(dsqrtk3T)). If the principal has much more limited information (as might often be the case for an external regulator or watchdog), and only observes the number of rounds in which members from each of the k groups were selected, but not the empirical estimates maintained by the myopic agent, the design of such a scheme becomes more complex. We show both positive and negative results in the classic and linear bandit settings by upper and lower bounding the cost of fair subsidy schemes.
{"title":"Fairness Incentives for Myopic Agents","authors":"Sampath Kannan, Michael Kearns, Jamie Morgenstern, Mallesh M. Pai, Aaron Roth, R. Vohra, Zhiwei Steven Wu","doi":"10.1145/3033274.3085154","DOIUrl":"https://doi.org/10.1145/3033274.3085154","url":null,"abstract":"We consider settings in which we wish to incentivize myopic agents (such as Airbnb landlords, who may emphasize short-term profits and property safety) to treat arriving clients fairly, in order to prevent overall discrimination against individuals or groups. We model such settings in both classical and contextual bandit models in which the myopic agents maximize rewards according to current empirical averages, but are also amenable to exogenous payments that may cause them to alter their choices. Our notion of fairness asks that more qualified individuals are never (probabilistically) preferred over less qualifie ones [8]. We investigate whether it is possible to design inexpensive subsidy or payment schemes for a principal to motivate myopic agents to play fairly in all or almost all rounds. When the principal has full information about the state of the myopic agents, we show it is possible to induce fair play on every round with a subsidy scheme of total cost o(T) (for the classic setting with k arms, ~{O}(sqrtk3T), and for the d-dimensional linear contextual setting ~{O}(dsqrtk3T)). If the principal has much more limited information (as might often be the case for an external regulator or watchdog), and only observes the number of rounds in which members from each of the k groups were selected, but not the empirical estimates maintained by the myopic agent, the design of such a scheme becomes more complex. We show both positive and negative results in the classic and linear bandit settings by upper and lower bounding the cost of fair subsidy schemes.","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114993743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Selfish routing is one of the fundamental models in the study of network traffic systems. While most literature assumes essentially static flows, game theoretical models of dynamic flows began to draw attention recently [1, 5]. We study a new dynamic flow game with atomic agents. The game is played over an acyclic directed network, with two special vertices called the origin o and the destination d, respectively, such that each edge is on at least one o-d path. Each edge of this network is associated with an integer capacity and a positive integer free-flow transit cost. Time horizon is infinite and discretized as 1,2,…. At each time point, a set of selfish agents enter the network from the origin, trying to reach the destination as quickly as possible. When an agent uses an edge, two costs are incurred to him: the fixed transit cost of the edge and a variable waiting cost dependent on the volume of the traffic flow on that edge and the edge capacity as well as the agent's position in the queue of agents waiting at that edge. The total cost to each agent, the latency he experiences in the network, is the sum of the two costs on all edges he uses (which form an o-d path in the network).
{"title":"A Network Game of Dynamic Traffic","authors":"Zhigang Cao, Bo Chen, Xujin Chen, Changjun Wang","doi":"10.1145/3033274.3085101","DOIUrl":"https://doi.org/10.1145/3033274.3085101","url":null,"abstract":"Selfish routing is one of the fundamental models in the study of network traffic systems. While most literature assumes essentially static flows, game theoretical models of dynamic flows began to draw attention recently [1, 5]. We study a new dynamic flow game with atomic agents. The game is played over an acyclic directed network, with two special vertices called the origin o and the destination d, respectively, such that each edge is on at least one o-d path. Each edge of this network is associated with an integer capacity and a positive integer free-flow transit cost. Time horizon is infinite and discretized as 1,2,…. At each time point, a set of selfish agents enter the network from the origin, trying to reach the destination as quickly as possible. When an agent uses an edge, two costs are incurred to him: the fixed transit cost of the edge and a variable waiting cost dependent on the volume of the traffic flow on that edge and the edge capacity as well as the agent's position in the queue of agents waiting at that edge. The total cost to each agent, the latency he experiences in the network, is the sum of the two costs on all edges he uses (which form an o-d path in the network).","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124045595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In light of the classic impossibility results of Arrow and Gibbard and Satterthwaite regarding voting with ordinal rules, there has been recent interest in characterizing how well common voting rules approximate the social optimum. In order to quantify the quality of approximation, it is natural to consider the candidates and voters as embedded within a common metric space, and to ask how much further the chosen candidate is from the population as compared to the socially optimal one. We use this metric preference model to explore a fundamental and timely question: does the social welfare of a population improve when candidates are representative of the population? If so, then by how much, and how does the answer depend on the complexity of the metric space? We restrict attention to the most fundamental and common social choice setting: a population of voters, two independently drawn candidates, and a majority rule election. When candidates are not representative of the population, it is known that the candidate selected by the majority rule can be thrice as far from the population as the socially optimal one; this holds even when the underlying metric is a line. We examine how this ratio improves when candidates are drawn independently from the population of voters. Our results are two-fold: When the metric is a line, the ratio improves from 3 to 4-2 √2}, roughly 1.1716; this bound is tight. When the metric is arbitrary, we show a lower bound of 1.5 and a constant upper bound strictly better than 2 on the approximation ratio of the majority rule. The positive result depends in part on the assumption that candidates are independent and identically distributed. However, we show that independence alone is not enough to achieve the upper bound: even when candidates are drawn independently, if the population of candidates can be different from the voters, then an upper bound of 2 on the approximation is tight. Thus, we show a constant gap between representative and non-representative candidates.
{"title":"Of the People: Voting Is More Effective with Representative Candidates","authors":"Yu Cheng, S. Dughmi, D. Kempe","doi":"10.1145/3033274.3085155","DOIUrl":"https://doi.org/10.1145/3033274.3085155","url":null,"abstract":"In light of the classic impossibility results of Arrow and Gibbard and Satterthwaite regarding voting with ordinal rules, there has been recent interest in characterizing how well common voting rules approximate the social optimum. In order to quantify the quality of approximation, it is natural to consider the candidates and voters as embedded within a common metric space, and to ask how much further the chosen candidate is from the population as compared to the socially optimal one. We use this metric preference model to explore a fundamental and timely question: does the social welfare of a population improve when candidates are representative of the population? If so, then by how much, and how does the answer depend on the complexity of the metric space? We restrict attention to the most fundamental and common social choice setting: a population of voters, two independently drawn candidates, and a majority rule election. When candidates are not representative of the population, it is known that the candidate selected by the majority rule can be thrice as far from the population as the socially optimal one; this holds even when the underlying metric is a line. We examine how this ratio improves when candidates are drawn independently from the population of voters. Our results are two-fold: When the metric is a line, the ratio improves from 3 to 4-2 √2}, roughly 1.1716; this bound is tight. When the metric is arbitrary, we show a lower bound of 1.5 and a constant upper bound strictly better than 2 on the approximation ratio of the majority rule. The positive result depends in part on the assumption that candidates are independent and identically distributed. However, we show that independence alone is not enough to achieve the upper bound: even when candidates are drawn independently, if the population of candidates can be different from the voters, then an upper bound of 2 on the approximation is tight. Thus, we show a constant gap between representative and non-representative candidates.","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114583514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider job scheduling settings, with multiple machines, where jobs arrive online and choose a machine selfishly so as to minimize their cost. Our objective is the classic makespan minimization objective, which corresponds to the completion time of the last job to complete. The incentives of the selfish jobs may lead to poor performance. To reconcile the differing objectives, we introduce posted machine prices. The selfish job seeks to minimize the sum of its completion time on the machine and the posted price for the machine. Prices may be static (i.e., set once and for all before any arrival) or dynamic (i.e., change over time), but they are determined only by the past, assuming nothing about upcoming events. Obviously, such schemes are inherently truthful. We consider the competitive ratio: the ratio between the makespan achievable by the pricing scheme and that of the optimal algorithm. We give tight bounds on the competitive ratio for both dynamic and static pricing schemes for identical, restricted, related, and unrelated machine settings. Our main result is a dynamic pricing scheme for related machines that gives a constant competitive ratio, essentially matching the competitive ratio of online algorithms for this setting. In contrast, dynamic pricing gives poor performance for unrelated machines. This lower bound also exhibits a gap between what can be achieved by pricing versus what can be achieved by online algorithms.
{"title":"Makespan Minimization via Posted Prices","authors":"M. Feldman, A. Fiat, A. Roytman","doi":"10.1145/3033274.3085129","DOIUrl":"https://doi.org/10.1145/3033274.3085129","url":null,"abstract":"We consider job scheduling settings, with multiple machines, where jobs arrive online and choose a machine selfishly so as to minimize their cost. Our objective is the classic makespan minimization objective, which corresponds to the completion time of the last job to complete. The incentives of the selfish jobs may lead to poor performance. To reconcile the differing objectives, we introduce posted machine prices. The selfish job seeks to minimize the sum of its completion time on the machine and the posted price for the machine. Prices may be static (i.e., set once and for all before any arrival) or dynamic (i.e., change over time), but they are determined only by the past, assuming nothing about upcoming events. Obviously, such schemes are inherently truthful. We consider the competitive ratio: the ratio between the makespan achievable by the pricing scheme and that of the optimal algorithm. We give tight bounds on the competitive ratio for both dynamic and static pricing schemes for identical, restricted, related, and unrelated machine settings. Our main result is a dynamic pricing scheme for related machines that gives a constant competitive ratio, essentially matching the competitive ratio of online algorithms for this setting. In contrast, dynamic pricing gives poor performance for unrelated machines. This lower bound also exhibits a gap between what can be achieved by pricing versus what can be achieved by online algorithms.","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131283399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the necessity of interaction for obtaining efficient allocations in combinatorial auctions with subadditive bidders. This problem was originally introduced by Dobzinski, Nisan, and Oren (STOC'14) as the following simple market scenario: m items are to be allocated among n bidders in a distributed setting where bidders valuations are private and hence communication is needed to obtain an efficient allocation. The communication happens in rounds: in each round, each bidder, simultaneously with others, broadcasts a message to all parties involved. At the end, the central planner computes an allocation solely based on the communicated messages. Dobzinski et al. showed that (at least some) interaction is necessary for obtaining any efficient allocation: no non-interactive (1-round) protocol with polynomial communication (in the number of items and bidders) can achieve approximation ratio better than Ω(m1/4), while for any r ≥ 1, there exists r-round protocols that achieve Ō(r. m1/r+1) approximation with polynomial communication; in particular, O(log m) rounds of interaction suffice to obtain an (almost) efficient allocation, i.e., a polylog(m)-approximation. A natural question at this point is to identify the "right" level of interaction (i.e., number of rounds) necessary to obtain an efficient allocation. In this paper, we resolve this question by providing an almost tight round-approximation tradeoff for this problem: we show that for any r ≥ 1, any r-round protocol that uses poly(m,n) bits of communication can only approximate the social welfare up to a factor of Ω(1 over r. m1/2 r+1). This in particular implies that Ω(log m over log log m) rounds of interaction are necessary for obtaining any efficient allocation (i.e., a constant or even a polylog(m)-approximation) in these markets. Our work builds on the recent multi-party round-elimination technique of Alon, Nisan, Raz, and Weinstein (FOCS'15) -- used to prove similar-in-spirit lower bounds for round-approximation tradeoff in unit-demand (matching) markets -- and settles an open question posed initially by Dobzinski et al., and subsequently by Alon et al.
研究了具有次可加投标人的组合拍卖中获得有效分配的相互作用的必要性。这个问题最初是由Dobzinski, Nisan和Oren (STOC'14)作为以下简单的市场场景提出的:m个项目将在分布式设置中的n个竞标者之间分配，竞标者的估值是私有的，因此需要沟通以获得有效的分配。这种通信是分轮进行的:在每一轮中，每个竞标者与其他竞标者同时向所有相关方广播一条消息。最后，中央计划器仅根据通信消息计算分配。Dobzinski等人表明，(至少一些)交互对于获得任何有效分配都是必要的:没有一个具有多项式通信的非交互(1轮)协议(在项目和投标人数量中)可以实现比Ω(m1/4)更好的近似比率，而对于任何r≥1，存在r轮协议，可以实现Ō(r)。多项式通信的M1 /r+1近似;特别是，O(log m)轮交互足以获得(几乎)有效的分配，即polylog(m)-近似。在这一点上，一个自然的问题是确定获得有效分配所需的“正确”交互级别(即回合数)。在本文中，我们通过为这个问题提供一个几乎紧密的圆形近似权衡来解决这个问题:我们表明，对于任何r≥1，任何使用多(m,n)位通信的r-圆形协议只能将社会福利近似到Ω(1 / r. m1/ r+1)的因子。这特别意味着Ω(log m / log log m)轮的相互作用对于在这些市场中获得任何有效分配(即，常数甚至是多元(m)近似)是必要的。我们的工作建立在最近由Alon、Nisan、Raz和Weinstein (FOCS’15)提出的多方消轮技术的基础上——该技术用于证明单位需求(匹配)市场中圆近似权衡的近似下限——并解决了最初由Dobzinski等人提出的一个开放问题，随后由Alon等人提出。
{"title":"Combinatorial Auctions Do Need Modest Interaction","authors":"Sepehr Assadi","doi":"10.1145/3033274.3085121","DOIUrl":"https://doi.org/10.1145/3033274.3085121","url":null,"abstract":"We study the necessity of interaction for obtaining efficient allocations in combinatorial auctions with subadditive bidders. This problem was originally introduced by Dobzinski, Nisan, and Oren (STOC'14) as the following simple market scenario: m items are to be allocated among n bidders in a distributed setting where bidders valuations are private and hence communication is needed to obtain an efficient allocation. The communication happens in rounds: in each round, each bidder, simultaneously with others, broadcasts a message to all parties involved. At the end, the central planner computes an allocation solely based on the communicated messages. Dobzinski et al. showed that (at least some) interaction is necessary for obtaining any efficient allocation: no non-interactive (1-round) protocol with polynomial communication (in the number of items and bidders) can achieve approximation ratio better than Ω(m1/4), while for any r ≥ 1, there exists r-round protocols that achieve Ō(r. m1/r+1) approximation with polynomial communication; in particular, O(log m) rounds of interaction suffice to obtain an (almost) efficient allocation, i.e., a polylog(m)-approximation. A natural question at this point is to identify the \"right\" level of interaction (i.e., number of rounds) necessary to obtain an efficient allocation. In this paper, we resolve this question by providing an almost tight round-approximation tradeoff for this problem: we show that for any r ≥ 1, any r-round protocol that uses poly(m,n) bits of communication can only approximate the social welfare up to a factor of Ω(1 over r. m1/2 r+1). This in particular implies that Ω(log m over log log m) rounds of interaction are necessary for obtaining any efficient allocation (i.e., a constant or even a polylog(m)-approximation) in these markets. Our work builds on the recent multi-party round-elimination technique of Alon, Nisan, Raz, and Weinstein (FOCS'15) -- used to prove similar-in-spirit lower bounds for round-approximation tradeoff in unit-demand (matching) markets -- and settles an open question posed initially by Dobzinski et al., and subsequently by Alon et al.","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125319557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Prior to 2014, the admission to Master's and PhD programs in psychology in Israel was a mostly decentralized process. In 2013, in response to concerns about the existing procedure, we proposed to use a mechanism that is both stable and strategy-proof for applicants. The first part of this paper describes how we successfully centralized this market, and the critical role of recent advances in the theory of matching with contracts. In the second part of the paper we show empirically (using clearinghouse data) and theoretically that the regularity in preferences with respect to contractual terms leads to a large core. Our results stand in sharp contrast to findings of previous studies on two-sided matching markets without contracts [2, 10, 11, 13]. During the design of the Israeli Psychology Master's Match (IPMM), we met with the faculty of each of the participating programs and asked about the way they choose between applicants. We discovered that departments' choice functions cannot be summarized by a quota and a rank-ordered list (ROL) for each program. Some departments employ affirmative action through minority quotas. Others aim to equalize the number of advisees each faculty member receives. And finally, some departments are willing to admit a limited number of applicants with different contractual terms (e.g., funding). Since terms can alter preferences between programs, this last feature implies that in order to satisfy the aforementioned desiderata, the applicants' message space must be expressive enough to convey their preferences over program-terms pairs. This market is therefore a special case of the matching-with-contracts model [9].
{"title":"Redesigning the Israeli Psychology Master's Match","authors":"A. Hassidim, Assaf Romm, Ran I. Shorrer","doi":"10.1145/3033274.3085124","DOIUrl":"https://doi.org/10.1145/3033274.3085124","url":null,"abstract":"Prior to 2014, the admission to Master's and PhD programs in psychology in Israel was a mostly decentralized process. In 2013, in response to concerns about the existing procedure, we proposed to use a mechanism that is both stable and strategy-proof for applicants. The first part of this paper describes how we successfully centralized this market, and the critical role of recent advances in the theory of matching with contracts. In the second part of the paper we show empirically (using clearinghouse data) and theoretically that the regularity in preferences with respect to contractual terms leads to a large core. Our results stand in sharp contrast to findings of previous studies on two-sided matching markets without contracts [2, 10, 11, 13]. During the design of the Israeli Psychology Master's Match (IPMM), we met with the faculty of each of the participating programs and asked about the way they choose between applicants. We discovered that departments' choice functions cannot be summarized by a quota and a rank-ordered list (ROL) for each program. Some departments employ affirmative action through minority quotas. Others aim to equalize the number of advisees each faculty member receives. And finally, some departments are willing to admit a limited number of applicants with different contractual terms (e.g., funding). Since terms can alter preferences between programs, this last feature implies that in order to satisfy the aforementioned desiderata, the applicants' message space must be expressive enough to convey their preferences over program-terms pairs. This market is therefore a special case of the matching-with-contracts model [9].","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"645 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132993856","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce a combinatorial variant of the cost sharing problem: several services can be provided to each player and each player values every combination of services differently. A publicly known cost function specifies the cost of providing every possible combination of services. A combinatorial cost sharing mechanism is a protocol that decides which services each player gets and at what price. We look for dominant strategy mechanisms that are (economically) efficient and cover the cost, ideally without overcharging (i.e., budget balanced). Note that unlike the standard cost sharing setting, combinatorial cost sharing is a multi-parameter domain. This makes designing dominant strategy mechanisms with good guarantees a challenging task. We present the Potential Mechanism -- a combination of the VCG mechanism and a well-known tool from the theory of cooperative games: Hart and Mas-Colell's potential function. The potential mechanism is a dominant strategy mechanism that always covers the incurred cost. When the cost function is subadditive the same mechanism is also approximately efficient. Our main technical contribution shows that when the cost function is submodular the potential mechanism is approximately budget balanced in three settings: supermodular valuations, symmetric cost function and general symmetric valuations, and two players with general valuations.
{"title":"Combinatorial Cost Sharing","authors":"Shahar Dobzinski, Shahar Ovadia","doi":"10.1145/3033274.3085141","DOIUrl":"https://doi.org/10.1145/3033274.3085141","url":null,"abstract":"We introduce a combinatorial variant of the cost sharing problem: several services can be provided to each player and each player values every combination of services differently. A publicly known cost function specifies the cost of providing every possible combination of services. A combinatorial cost sharing mechanism is a protocol that decides which services each player gets and at what price. We look for dominant strategy mechanisms that are (economically) efficient and cover the cost, ideally without overcharging (i.e., budget balanced). Note that unlike the standard cost sharing setting, combinatorial cost sharing is a multi-parameter domain. This makes designing dominant strategy mechanisms with good guarantees a challenging task. We present the Potential Mechanism -- a combination of the VCG mechanism and a well-known tool from the theory of cooperative games: Hart and Mas-Colell's potential function. The potential mechanism is a dominant strategy mechanism that always covers the incurred cost. When the cost function is subadditive the same mechanism is also approximately efficient. Our main technical contribution shows that when the cost function is submodular the potential mechanism is approximately budget balanced in three settings: supermodular valuations, symmetric cost function and general symmetric valuations, and two players with general valuations.","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"182 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131255428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Small changes to the parameters of a system can lead to abrupt qualitative changes of its behavior, a phenomenon known as bifurcation. Such instabilities are typically considered problematic, however, we show that their power can be leveraged to design novel types of mechanisms. Hysteresis mechanisms use transient changes of system parameters to induce a permanent improvement to its performance via optimal equilibrium selection. Optimal control mechanisms induce convergence to states whose performance is better than even the best equilibrium. We apply these mechanisms in two different settings that illustrate the versatility of bifurcation mechanism design. In the first one we explore how introducing flat taxation can improve social welfare, despite decreasing agent "rationality", by destabilizing inefficient equilibria. From there we move on to consider a well known game of tumor metabolism and use our approach to derive novel cancer treatment strategies.
{"title":"Bifurcation Mechanism Design - from Optimal Flat Taxes to Improved Cancer Treatments","authors":"Ger Yang, G. Piliouras, D. Basanta","doi":"10.1145/3033274.3085144","DOIUrl":"https://doi.org/10.1145/3033274.3085144","url":null,"abstract":"Small changes to the parameters of a system can lead to abrupt qualitative changes of its behavior, a phenomenon known as bifurcation. Such instabilities are typically considered problematic, however, we show that their power can be leveraged to design novel types of mechanisms. Hysteresis mechanisms use transient changes of system parameters to induce a permanent improvement to its performance via optimal equilibrium selection. Optimal control mechanisms induce convergence to states whose performance is better than even the best equilibrium. We apply these mechanisms in two different settings that illustrate the versatility of bifurcation mechanism design. In the first one we explore how introducing flat taxation can improve social welfare, despite decreasing agent \"rationality\", by destabilizing inefficient equilibria. From there we move on to consider a well known game of tumor metabolism and use our approach to derive novel cancer treatment strategies.","PeriodicalId":287551,"journal":{"name":"Proceedings of the 2017 ACM Conference on Economics and Computation","volume":"109 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129672810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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